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🔗 Mathematics

In topology, the long line (or Alexandroff line) is a topological space somewhat similar to the real line, but in a certain way "longer". It behaves locally just like the real line, but has different large-scale properties (e.g., it is neither Lindelöf nor separable). Therefore, it serves as one of the basic counterexamples of topology. Intuitively, the usual real-number line consists of a countable number of line segments [0, 1) laid end-to-end, whereas the long line is constructed from an uncountable number of such segments.

🔗 Mathematics

The 15-puzzle (also called Gem Puzzle, Boss Puzzle, Game of Fifteen, Mystic Square and many others) is a sliding puzzle that consists of a frame of numbered square tiles in random order with one tile missing. The puzzle also exists in other sizes, particularly the smaller 8-puzzle. If the size is 3×3 tiles, the puzzle is called the 8-puzzle or 9-puzzle, and if 4×4 tiles, the puzzle is called the 15-puzzle or 16-puzzle named, respectively, for the number of tiles and the number of spaces. The object of the puzzle is to place the tiles in order by making sliding moves that use the empty space.

The n-puzzle is a classical problem for modelling algorithms involving heuristics. Commonly used heuristics for this problem include counting the number of misplaced tiles and finding the sum of the taxicab distances between each block and its position in the goal configuration. Note that both are admissible, i.e. they never overestimate the number of moves left, which ensures optimality for certain search algorithms such as A*.

🔗 Systems 🔗 Systems/Chaos theory

In mathematics, the Menger sponge (also known as the Menger cube, Menger universal curve, Sierpinski cube, or Sierpinski sponge) is a fractal curve. It is a three-dimensional generalization of the one-dimensional Cantor set and two-dimensional Sierpinski carpet. It was first described by Karl Menger in 1926, in his studies of the concept of topological dimension.

🔗 Astronomy

A Messier marathon is an attempt, usually organized by amateur astronomers, to find as many Messier objects as possible during one night. The Messier catalogue was compiled by French astronomer Charles Messier during the late 18th century and consists of 110 relatively bright deep-sky objects (galaxies, nebulae, and star clusters).

🔗 Fencing

Dueling scars (German: Schmisse) have been seen as a "badge of honour" since as early as 1825. Known variously as "Mensur scars", "the bragging scar", "smite", "Schmitte" or "Renommierschmiss", dueling scars were popular amongst upper-class Austrians and Germans involved in academic fencing at the start of the 20th century. Being a practice amongst university students, it was seen as a mark of their class and honour, due to the status of dueling societies at German and Austrian universities at the time, and is an early example of scarification in European society. The practice of dueling and the associated scars was also present to some extent in the German military.

Foreign tourists visiting Germany in the late 19th century were shocked to see the students, generally with their Studentcorps, at major German universities such as Heidelberg, Bonn, or Jena with facial scars – some older, some more recent, and some still wrapped in bandages.

The sport of academic fencing at the time was very different from modern fencing using specially developed swords. The so-called Mensurschläger (or simply Schläger, "hitter") existed in two versions. The most common weapon is the Korbschläger with a basket-type guard. In some universities in the eastern part of Germany, the so-called Glockenschläger is in use which is equipped with a bell-shaped guard. The individual duels between students, known as Mensuren, were somewhat ritualised. In some cases, protective clothing was worn, including padding on the arm and an eye guard.

The culture of dueling scars was mainly common to Germany and Austria, to a lesser extent some central European countries and briefly at places such as Oxford and some other elite universities. German military laws permitted men to wage duels of honor until World War I. During the Third Reich the Mensur was prohibited at all Universities following the partyline.

Within the duel, it was seen as ideal and a way of showing courage to be able to stand and take the blow, as opposed to inflicting the wound. It was important to show one's dueling prowess, but also that one was capable of taking the wound that was inflicted.

🔗 United States 🔗 California 🔗 Disaster management 🔗 Oregon 🔗 United States/Utah 🔗 Weather 🔗 Weather/Non-tropical storms 🔗 Weather/Floods

The Great Flood of 1862 was the largest flood in the recorded history of Oregon, Nevada, and California, occurring from December 1861 to January 1862. It was preceded by weeks of continuous rains and snows in the very high elevations that began in Oregon in November 1861 and continued into January 1862. This was followed by a record amount of rain from January 9–12, and contributed to a flood that extended from the Columbia River southward in western Oregon, and through California to San Diego, and extended as far inland as Idaho in the Washington Territory, Nevada and Utah in the Utah Territory, and Arizona in the western New Mexico Territory. The event dumped an equivalent of 10 feet (3.0 m) of water in California, in the form of rain and snow, over a period of 43 days. Immense snowfalls in the mountains of far western North America caused more flooding in Idaho, Arizona, New Mexico, as well as in Baja California and Sonora, Mexico the following spring and summer, as the snow melted.

The event was capped by a warm intense storm that melted the high snow load. The resulting snow-melt flooded valleys, inundated or swept away towns, mills, dams, flumes, houses, fences, and domestic animals, and ruined fields. It has been described as the worst disaster ever to strike California. The storms caused approximately $100 million (1861 USD) in damage, approximately equal to $3.117 billion (2021 USD). The governor, state legislature, and state employees were not paid for a year and a half. At least 4,000 people were estimated to have been killed in the floods in California, which was roughly 1% of the state population at the time.

🔗 Psychology 🔗 Education

Bloom's taxonomy is a set of three hierarchical models used to classify educational learning objectives into levels of complexity and specificity. The three lists cover the learning objectives in cognitive, affective and sensory domains. The cognitive domain list has been the primary focus of most traditional education and is frequently used to structure curriculum learning objectives, assessments and activities.

The models were named after Benjamin Bloom, who chaired the committee of educators that devised the taxonomy. He also edited the first volume of the standard text, Taxonomy of Educational Objectives: The Classification of Educational Goals.

🔗 Mathematics 🔗 Statistics

In the design of experiments in statistics, the lady tasting tea is a randomized experiment devised by Ronald Fisher and reported in his book The Design of Experiments (1935). The experiment is the original exposition of Fisher's notion of a null hypothesis, which is "never proved or established, but is possibly disproved, in the course of experimentation".

The example is loosely based on an event in Fisher's life. The woman in question, phycologist Muriel Bristol, claimed to be able to tell whether the tea or the milk was added first to a cup. Her future husband, William Roach, suggested that Fisher give her eight cups, four of each variety, in random order. One could then ask what the probability was for her getting the specific number of cups she identified correct (in fact all eight), but just by chance.

Fisher's description is less than 10 pages in length and is notable for its simplicity and completeness regarding terminology, calculations and design of the experiment. The test used was Fisher's exact test.

🔗 Disaster management

The preparedness paradox is the proposition that if a society or individual acts effectively to mitigate a potential disaster such as a pandemic, natural disaster or other catastrophe so that it causes less harm, the avoided danger will be perceived as having been much less serious because of the limited damage actually caused. The paradox is the incorrect perception that there had been no need for careful preparation as there was little harm, although in reality the limitation of the harm was due to preparation. Several cognitive biases can consequently hamper proper preparation for future risks.

Bohm Dialogue (also known as Bohmian Dialogue or "Dialogue in the Spirit of David Bohm") is a freely flowing group conversation in which participants attempt to reach a common understanding, experiencing everyone's point of view fully, equally and nonjudgementally. This can lead to new and deeper understanding. The purpose is to solve the communication crises that face society, and indeed the whole of human nature and consciousness. It utilizes a theoretical understanding of the way thoughts relate to universal reality. It is named after physicist David Bohm who originally proposed this form of dialogue.